Jessica is 20 years younger than Ishaan. Ishaan and Jessica first met 3 years ago. Seventeen years ago, Ishaan was 5 times as old as Jessica. How old is Ishaan now?
We can use the given information to write down two equations that describe the ages of Ishaan and Jessica. Let Ishaan's current age be $i$ and Jessica's current age be $j$ The information in the first sentence can be expressed in the following equation: $i = j + 20$ Seventeen years ago, Ishaan was $i - 17$ years old, and Jessica was $j - 17$ years old. The information in the second sentence can be expressed in the following equation: $i - 17 = 5(j - 17)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $i$ , it might be easiest to solve our first equation for $j$ and substitute it into our second equation. Solving our first equation for $j$ , we get: $j = i - 20$ . Substituting this into our second equation, we get the equation: $i - 17 = 5($ $(i - 20)$ $ -$ $ 17)$ which combines the information about $i$ from both of our original equations. Simplifying the right side of this equation, we get: $i - 17 = 5i - 185$ Solving for $i$ , we get: $4 i = 168$ $i = 42$.